A simple way to visualize event-by-event average pT fluctuations is by assuming that each collision has a different temperature parameter (inverse pT slope) and that the ensemble of events has a temperature distribution about the mean, less than T greater than , with standard deviation sigmaT. PHENIX characterizes the non-random fluctuation of MpT, the event-by-event average pT, by FpT, the fractional difference of the standard deviation of the data from that of a random sample obtained with mixed events. This can be related to the temperature fluctuation: FpT = sigmaMpTdata/sigmaMpTrandom - 1 ~ (less than eta greated than-1)sigmaT 2/ less thanT greated than 2. Combining this with the Gavai et al. [5] and Korus et al. [6] definitions of the specific heat per particle, a simple relationship is obtained: cv/T3 = less than eta greated than/less than Ntot greated than )Ĺ(1/FpT). FpT is measured with a fraction less than eta greated than)Ntot* of the total particles produced, a purely geometrical factor representing the fractional acceptance, ~1/33 in PHENIX. Gavai et al. [5] predict that cv/T3 = 15, which corresponds to FpT ~ 0.20% in PHENIX, which may be accessible by measurements of MpT in the range 0.2 d pT d 0.6 GeV/c. In order to test the Gavai et al. prediction that cv/T3 is reduced in a QGP compared to the ideal gas value (15 compared to 21), precision measurements of FpT in the range 0.20% for 0.2 less-than or equal to pT greater-than or equal to 0.6 GeV/c may be practical.
In this study, we analyze the recently proposed charge transfer fluctuations within a finite pseudorapidity space. As the charge transfer fluctuation is a measure of the local charge correlation length, it is capable of detecting inhomogeneity in the hot and dense matter created by heavy-ion collisions. We predict that going from peripheral to central collisions, the charge transfer fluctuations at midrapidity should decrease substantially while the charge transfer fluctuations at the edges of the observation window should decrease by a small amount. These are consequences of having a strongly inhomogeneous matter where the QGP component is concentrated around midrapidity. We also show how to constrain the values of the charge correlations lengths in both the hadronic phase and the QGP phase using the charge transfer fluctuations. Current manuscript is based on the two recent papers [10, 13].
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